Question

check whether 5, - 2, 6, 4 and 7 - 2 are the vertices of an isosceles triangle​

Answer 1

Let the points (5, −2), (6, 4), and (7, −2) are representing the vertices A, B, and C of the given triangle respectively.

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refer the above pic

As two sides are equal in length, therefore, ABCis an isosceles triangle.

Answer 2

Answer:

Put:     A = ( 5, -2 )        B = ( 6, 4 )        C = ( 7, -2 )

Method 1   ---  Calculating lengths

AB = √( (6 - 5)² + (4 - -2)² ) = √( 1² + 6² ) = √37

BC = √( (6 - 7)² + (4 - -2)² ) = √( 1² + 6² ) = √37

As AB = BC, the triangle ABC is isosceles

Method 2  ---  Symmetry

The midpoint of AC is ( (5+7)/2, -2 ) = ( 6, -2 ).

Since A and C have the same y-coordinate, the line is horizontal.

So the perpendicular bisector of AC is the line x = 6.

Since the x-coordinate of B is 6, the point B is on the perpendicular bisector of AC.

Therefore ABC is an isosceles triangle.